Solve 5left(19-xright)/6x+4(19-x)=2/3

$$\frac{ 5 \left( 19-x \right) }{ 6x+4(19-x) } = \frac{ 2 }{ 3 }$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

Variable x cannot be equal to -38 since division by zero is not defined. Multiply both sides of the equation by 6\left(x+38\right), the least common multiple of 6x+4\left(19-x\right),3.

$$3\times 5\left(19-x\right)=4\left(x+38\right)$$

Multiply 3 and 5 to get 15.

$$15\left(19-x\right)=4\left(x+38\right)$$

Use the distributive property to multiply 15 by 19-x.

$$285-15x=4\left(x+38\right)$$

Use the distributive property to multiply 4 by x+38.

$$285-15x=4x+152$$

Subtract 4x from both sides.

$$285-15x-4x=152$$

Combine -15x and -4x to get -19x.

$$285-19x=152$$

Subtract 285 from both sides.

$$-19x=152-285$$

Subtract 285 from 152 to get -133.

$$-19x=-133$$

Divide both sides by -19.

$$x=\frac{-133}{-19}$$

Divide -133 by -19 to get 7.

$$x=7$$